A spectral Szego theorem on the real line

Abstract

We characterize even measures $\mu =wdx+{\mu }_s$ on the real line with finite entropy integral ${\int }_R\frac{\log w(t)}{1+t^2}dt>-\infty$ in terms of $2\times 2$ Hamiltonian generated by $\mu$ in the sense of inverse spectral theory. As a corollary, we obtain criterion for spectral measure of Krein string to have converging logarithmic integral.

References in corpus (2)

• Canonical systems and de Branges spaces
• Wiener-Hopf operators admit triangular factorization

Cited by in corpus (7)

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• On the absolutely continuous spectrum of generalized indefinite strings II
• Entropy function and orthogonal polynomials
• Sobolev norms of $L^2$-solutions to NLS